Manager Danny Wilson has added free agents Tony McMahon and Matt Hill as well as Crewe Alexandra's Shaun Miller to his squad.
The deals come just days after the Blades secured the services of Chris Porter and Kevin McDonald on new contracts.
Hill, who impressed in a loan spell with United last term, has penned a two-year deal with the club after his release from Blackpool, as has former Middlesbrough man and fellow defender McMahon.
Forward Miller, 24, who moves to Bramhall lane for an undisclosed fee, has agreed a two-year stay in South Yorkshire with the option of a third.
All three could be in line to make their debut against local rivals Rotherham at the New York Stadium on Tuesday.
- Shaun Miller
- Crewe Alexandra
- Matt Hill